Question

There is a monoatomic cubic structure with identical atoms at the corners, one third the way up the four vertical walls (for a total of 4 atoms up the vertical walls), and a body atom sitting 3/4 the way up (1/2 , 1/2, 2/3). (A total of 13 atoms). r=1 and Å=0.1nm.

Find:

(i) reciprocal lattice vectors

(ii) structure factor

(iii) a table of relative intensities as a function of the h,k,l values for the first four rings

(iv) What are the shifts in the peak positions for diffraction from a (011) plane with 0.1nm radiation if the thermal coefficient is the same as for 1h and the sample is heated to 1000K.

Answer 1

For a monoatomic cubic structure:

a2 × a3 a2 a1 .(a2 × a3 ) similarly

there are four lattice sites within each cubic cell so,

$\vec{R_1}=0,\vec{R_2}=\frac{a}{2}(\hat{x}+\hat{y}),\vec{R_3}=\frac{a}{2}(\hat{y}+\hat{z}),\vec{R_4}=\frac{a}{2}(\hat{z}+\hat{x})$

Now the Structure factor is given by

where

so

$S=\sum_{i=1}^{4}exp(i\vec{G}.\vec{R_i})=1+exp[i\pi(h+k)]+exp[i\pi(k+l)]+exp[i\pi(l+h)]$

33. 72.46 3623 | 1.303 0.5917 9.

2θ-26.529 37.85° 61.70 68.35 46.81 86.94° 54.60° 80.88